Implement a class Vector that represents a mathematical vector in 2D space. The class should have methods for vector addition, subtraction, dot product, and cross product.
Example 1:
Input: v1 = Vector(1, 2) v2 = Vector(2, 3) print(v1.add(v2)) print(v1.subtract(v2)) print(v1.dot(v2)) print(v1.cross(v2)) Output: Vector(3, 5) Vector(-1, -1) 8 -1
In 2D space, the dot product of vectors (a, b) and (c, d) is (ac + bd) and the cross product is (ad – bc).
class Vector:
def __init__(self, x, y):
self.x = x
self.y = y
def __str__(self):
return f"Vector({self.x}, {self.y})"
def add(self, other):
return Vector(self.x + other.x, self.y + other.y)
def subtract(self, other):
return Vector(self.x - other.x, self.y - other.y)
def dot(self, other):
return self.x * other.x + self.y * other.y
def cross(self, other):
return self.x * other.y - self.y * other.x
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